Music Theory · Chords

Chord Construction Methods

How any chord — from a basic triad to a stacked 13th — is built from intervals. Learn the universal formula method and you can construct any chord on the piano without memorizing them one at a time.

How chords are built

Every chord in Western tonal music — every triad, every 7th, every dense jazz extended chord — is built by stacking intervals above a root note. The intervals you choose, and how many you stack, determine the chord's quality, color, and function. Master one short list of interval formulas and you no longer need to memorize chord shapes one by one — you can build any chord, in any key, from first principles.

The most universal building convention is stacking thirds: each new note sits a major or minor third above the previous one. A triad is three stacked thirds. A 7th chord is four stacked thirds. A 13th chord is seven. The pattern always continues upward by thirds, just with more tones on top.

A second, equally important method uses scale degrees: number the notes of a major scale 1 through 7, and a chord is defined by which scale degrees it includes. C major (1-3-5), C7 (1-3-5-♭7), Cmaj7 (1-3-5-7), C9 (1-3-5-♭7-9). Both methods describe the same chords from different angles — interval-stacking shows you the shape on the keyboard; scale-degree thinking shows you the function within a key.

The big idea

A chord symbol is a formula. The letter names the root, the suffix tells you which intervals to stack on top. Learn ten or twelve formulas and you can build hundreds of chords.

The stacking-thirds method

Watch a Cmaj9 chord build itself one third at a time. Each step adds one more interval to the stack. By the time you reach step 5, the chord spans an octave and a step — but it was built from a single rule: another third on top.

Start with the root: C

Root

Root3rd5th7th9th

Every chord begins with a root — the note that names the chord. We start on C, the fifth-line space on the bass clef and the white key just left of the two black keys.

The two thirds you alternate decide the quality. Major 3rd then minor 3rd = major triad. Minor 3rd then major 3rd = minor triad. Two minor thirds = diminished. Two major thirds = augmented. Once you reach the 7th and 9th, the same alternation continues — different combinations give Cmaj7, C7, Cm7, C7♭9, and so on.

Formulas for every chord quality

Memorize the column labeled “Formula” below and you can build any of these chord types on any root. Half steps are counted from the root; the “scale degrees” column references the major scale of the root.

Chord	Symbol	Formula (intervals)	Scale degrees	Example in C
Major	C	R · M3 · P5	1 – 3 – 5	C – E – G
Minor	Cm	R · m3 · P5	1 – ♭3 – 5	C – E♭ – G
Diminished	Cdim	R · m3 · ♭5	1 – ♭3 – ♭5	C – E♭ – G♭
Augmented	Caug	R · M3 · ♯5	1 – 3 – ♯5	C – E – G♯
Sus2	Csus2	R · M2 · P5	1 – 2 – 5	C – D – G
Sus4	Csus4	R · P4 · P5	1 – 4 – 5	C – F – G
Dominant 7	C7	R · M3 · P5 · m7	1 – 3 – 5 – ♭7	C – E – G – B♭
Major 7	Cmaj7	R · M3 · P5 · M7	1 – 3 – 5 – 7	C – E – G – B
Minor 7	Cm7	R · m3 · P5 · m7	1 – ♭3 – 5 – ♭7	C – E♭ – G – B♭
Minor 7♭5 (half-dim)	Cø / Cm7♭5	R · m3 · ♭5 · m7	1 – ♭3 – ♭5 – ♭7	C – E♭ – G♭ – B♭
Diminished 7	Cdim7	R · m3 · ♭5 · ♭♭7	1 – ♭3 – ♭5 – 𝄫7	C – E♭ – G♭ – B𝄫 (= A)

How to read the formulas: R = root, M3 = major 3rd (4 half steps from root), m3 = minor 3rd (3 half steps), P5 = perfect 5th (7 half steps), ♭5 = diminished 5th (6 half steps), ♯5 = augmented 5th (8 half steps), m7 = minor 7th (10 half steps), M7 = major 7th (11 half steps).

Extensions — 7, 9, 11, and 13

Beyond the triad, every additional note continues stacking thirds: 7th, then 9th, then 11th, then 13th. By the time you reach the 13th you have stacked all seven notes of the parent scale on top of one another.

7th — one third above the 5th. Major or minor depending on the chord type.
9th — the 2nd scale degree raised an octave. Adds shimmer and color above the 7th.
11th — the 4th scale degree raised an octave. In dominant chords usually sharped (♯11) to avoid clashing with the 3rd; in minor chords used naturally.
13th — the 6th scale degree raised an octave. The top of the stack. A C13 chord has so many notes that piano voicings usually omit a few (most commonly the perfect 5th).

Important convention: a chord symbol that lists a higher extension implies all the lower ones unless explicitly altered. C13 means C – E – G – B♭ – D – F – A. But in practice pianists rarely play all seven notes; voicings drop redundant or clashing tones. The chord symbol describes the harmonic content, not the literal note-by-note layout.

Altered tones — ♭5, ♯5, ♭9, ♯9, ♯11

An alteration is a chromatic change to an extension. The chord symbol lists the alteration in parentheses or after the chord name. Alterations are most common on dominant 7th chords, where they create the tense, “outside” sound jazz musicians use to drive a V → I resolution.

♭5 — lower the 5th a half step. Yields tritone color.
♯5 — raise the 5th a half step (same as augmented). Common in dominant 7♯5 chords.
♭9 — lower the 9th a half step. The most pungent dissonance on a dominant chord; resolves down a half step into the new tonic.
♯9 — raise the 9th a half step (enharmonically a minor 3rd above the root). Famous from Jimi Hendrix's “Purple Haze” (E7♯9).
♯11 — raise the 11th a half step (a Lydian-flavored color tone). Used on both dominant and major chords in jazz.

A “fully altered” dominant chord — C7alt — combines several alterations at once: ♭9, ♯9, ♭5 (= ♯11), ♯5 (= ♭13). The result is the sound of the altered scale, the workhorse of post-1940s jazz dominant harmony.

The scale-degree method

The interval method tells you exactly which notes go in the chord. The scale-degree method tells you the same thing in a more compact notation: write the chord as a set of numbers relative to the major scale of the root.

C major scale: C(1) – D(2) – E(3) – F(4) – G(5) – A(6) – B(7). Any C-root chord can now be described as a subset of those degrees:

C major = 1-3-5
Cm = 1-♭3-5
C7 = 1-3-5-♭7
Cmaj9 = 1-3-5-7-9
Cm11 = 1-♭3-5-♭7-9-11
C7♯11 = 1-3-5-♭7-9-♯11
C13 = 1-3-5-♭7-9-11-13

This is the notation method most commonly used in modern jazz education and software. To play the chord, count up the major scale of the root (in this case, C major), apply the flats and sharps, and you have the note set.

A 4-step workflow for building any chord

Given any chord symbol — say, “F♯m7♭5” — here is the algorithm that produces the notes:

Identify the root. Read the letter name (and accidental). For F♯m7♭5, the root is F♯.
Decode the suffix into a formula. “m7♭5” = minor triad + minor 7th + flatted 5th = 1-♭3-♭5-♭7.
Apply the formula to the root's major scale. F♯ major: F♯-G♯-A♯-B-C♯-D♯-E♯. Take 1-♭3-♭5-♭7: F♯ – A (♭3 from F♯) – C (♭5) – E (♭7). That is the chord.
Voice it on the piano. Distribute the notes across the hands — root and 7th in the left, 3rd and 5th in the right, or any inversion you prefer. The chord identity is the note set; the voicing is the layout.

Test your understanding

Triad construction is the foundation of all chord building. Five questions drawn from a larger bank — chord qualities, intervals, and chord-symbol decoding.

📝Triad Construction Quiz

Test your understanding with 5 quick questions.

Frequently asked questions

Why are chords built by stacking thirds and not other intervals?

Because thirds — major and minor — are consonant intervals that blend pleasantly when stacked. Stacking fourths creates quartal harmony (modern jazz, Bill Evans), and stacking fifths creates open, "power chord" sonorities. But thirds are the standard in tonal music because they produce the smoothest blends. Most chord theory you encounter assumes tertian (third-based) construction.

What does the small "m" mean in a chord symbol?

Lowercase "m" always means minor — specifically, that the chord has a minor 3rd above the root instead of a major 3rd. "Cm" is a C minor triad. "Cm7" is a C minor 7th chord. Note that "maj" (with a "j") is something different: it specifies a major 7th interval, as in "Cmaj7." A bare "C7" by convention means a dominant 7th, which has a minor 7th interval — so the absence of "maj" is meaningful.

Do I have to memorize chord symbols, or can I just calculate them?

Both, eventually. Calculate first — that builds understanding and lets you handle any chord you encounter. After enough repetition, the most common symbols (maj7, m7, 7, m7♭5, dim7, sus4, 9, 13) become instant — your hand goes to them without thinking. Memorizing without understanding is brittle; calculating without internalizing is slow. Aim for both.

Why do some chord symbols omit certain notes?

Because higher extensions imply lower ones, and piano voicings rarely include every note in the implied stack. A C13 voicing typically omits the 5th and sometimes the 11th. The chord symbol describes the harmonic identity; what you play is a practical voicing. As long as the essential color tones (root, 3rd, 7th, and the named extension) are present, the chord still sounds like the symbol.

What is the difference between a sus chord and an alteration?

A sus (suspended) chord REPLACES the 3rd with another note — sus2 uses the 2nd instead of the 3rd; sus4 uses the 4th instead of the 3rd. The 3rd is gone, not just modified. An alteration (♭5, ♯9, etc.) MODIFIES an existing chord tone; the rest of the chord remains. Csus4 is C-F-G (no 3rd). C7♭9 is C-E-G-B♭-D♭ (still has the 3rd, plus an altered 9th).

How do I build a chord on a black-key root like F♯ or E♭?

Same procedure — the root is just a different starting point. F♯m: build F♯ major scale (F♯-G♯-A♯-B-C♯-D♯-E♯), apply 1-♭3-5, get F♯-A-C♯. E♭7: build E♭ major scale (E♭-F-G-A♭-B♭-C-D), apply 1-3-5-♭7, get E♭-G-B♭-D♭. The black-key chord pages on piano.org show every chord pre-built if you want a reference, but doing the math from the formula is how you internalize the system.